On the NES or SNES and any console with a dpad like those (which was patented by nintendo so until that expired there were other designed), it's actually just physically impossible. The directions are on a physical rocker that can't be pressed in two parallel directions at once.
Though if the controller pcb is really worn down by the rocker's center nub, it can start to become possible, and then there really is nothing stopping you. It's not uncommon for really well-loved controllers to end up like this.
It's definitely a letter-of-the-law thing where you could claim "but it's an original controller!" but no speedrun leaderboard is gonna let you get away with it.
Also I don't think emulators do a neutral input if you press both, that would be quite weird (and unlike how it happens with a real controller when you move from one to the other). Instead I think they prioritize the first input.